Compound Measures: WJEC GCSE Numeracy Higher June 2025 Unit 1 Q4

Numeracy Higher June 2025 Unit 1 Q4

WJECHigherCurrent spec6 marksCompound Measures Units & Time

4. When Hassan has a bath, he fills it with 30 gallons of water.
When Hassan has a shower, water flows from his shower at a rate of 0·2 litres per second.
Hassan uses the same amount of water whether he has a bath or a shower.

How long does he spend in the shower?
Give your answer in minutes and seconds.
You must show all your working. [6]

Use: 1 gallon ≈ 4·5 litres

Time in the shower is …………… minutes …………… seconds

Mark scheme

Scheme	Marks	Comments
(Number of minutes in the shower) (30 × 4.5 ÷ 0.2) ÷ 60 30 × 4.5 × 5 ÷ 60 or equivalent	M3	Complete unspoilt method, may be seen in stages Allow an implied M3 from appropriate sight of one of the following: 675 with an answer between 10 minutes and 12 minutes ‘their 30 × 4.5 ÷ 0.2’ incorrectly evaluated with a suitable answer in minutes that implies division by 60 M2 for any one of the following, may be seen in stages with no more than 1 additional incorrect stage: 30 × 4.5 ÷ 0.2 (= 675) 30 × 4.5 ÷ 60 (= 2.25)* (30 ÷ 0.2) ÷ 60 (= 2.5)* (4.5 ÷ 0.2) ÷ 60 (= 0.375)* 30 × 4.5 (= 135) and 0.2 × 60 (= 12) *Allow an implied M2 from incorrect calculation of 30 × 4.5, 30 ÷ 0.2 or 4.5 ÷ 0.2 followed by an answer that implies division by 60 M1 for any one of the following, may be seen in stages with additional incorrect stages: 30 × 4.5 (= 135) 4.5 ÷ 0.2 (= 45 ÷ 2 = 4.5 × 5 ) (= 22.5) 0.2 ÷ 4.5 (= 0.044…) 30 ÷ 0.2 (= 30 × 5 ) (= 150) 0.2 × 60 (= 60 ÷ 5) (= 12)
11 minutes 15 seconds	A3	CAO. Answer space takes precedence A2 for any one of the following, from correct working: 11.25 (minutes) or \(11\frac{1}{4}\) (minutes) 11.15 (minutes) or 11 minutes 25 seconds (30 × 4.5 ÷ 0.2 =) 675 (seconds) FT from M3 for ‘their number of minutes and seconds’ calculated accurately following from 1 error in calculation in the complete method, 30 × 4.5 ÷ 0.2 (with 1 product or 1 division incorrectly evaluated) A1 for any one of the following that may be implied by further calculation: (30 × 4.5 =) 135 (litres) (4.5 ÷ 0.2 =) 22.5 (seconds per gallon) (0.2 ÷ 4.5 =) 0.044… (gallons per second) (30 ÷ 0.2 =) 150 (0.2 × 60 = ) 12 (litres per minute) (30 × 4.5 ÷ 60 =) 2.25 ((30 ÷ 0.2) ÷ 60 =) 2.5 ((4.5 ÷ 0.2) ÷ 60 =) 0.375 (minutes per gallon) FT from an incorrect division or multiplication for further appropriate product or division correctly evaluated

Scheme

Marks

Comments

(Number of minutes in the shower)
(30 × 4.5 ÷ 0.2) ÷ 60
30 × 4.5 × 5 ÷ 60 or equivalent

Complete unspoilt method, may be seen in stages
Allow an implied M3 from appropriate sight of one of the following:

675 with an answer between 10 minutes and 12 minutes
‘their 30 × 4.5 ÷ 0.2’ incorrectly evaluated with a suitable answer in minutes that implies division by 60

M2 for any one of the following, may be seen in stages with no more than 1 additional incorrect stage:

30 × 4.5 ÷ 0.2 (= 675)
30 × 4.5 ÷ 60 (= 2.25)*
(30 ÷ 0.2) ÷ 60 (= 2.5)*
(4.5 ÷ 0.2) ÷ 60 (= 0.375)*
30 × 4.5 (= 135) and 0.2 × 60 (= 12)

*Allow an implied M2 from incorrect calculation of 30 × 4.5, 30 ÷ 0.2 or 4.5 ÷ 0.2 followed by an answer that implies division by 60

M1 for any one of the following, may be seen in stages with additional incorrect stages:

30 × 4.5 (= 135)
4.5 ÷ 0.2 (= 45 ÷ 2 = 4.5 × 5 ) (= 22.5)
0.2 ÷ 4.5 (= 0.044…)
30 ÷ 0.2 (= 30 × 5 ) (= 150)
0.2 × 60 (= 60 ÷ 5) (= 12)

11 minutes 15 seconds

CAO. Answer space takes precedence

A2 for any one of the following, from correct working:

11.25 (minutes) or \(11\frac{1}{4}\) (minutes)
11.15 (minutes) or 11 minutes 25 seconds
(30 × 4.5 ÷ 0.2 =) 675 (seconds)
FT from M3 for ‘their number of minutes and seconds’ calculated accurately following from 1 error in calculation in the complete method,
30 × 4.5 ÷ 0.2
(with 1 product or 1 division incorrectly evaluated)

A1 for any one of the following that may be implied by further calculation:

(30 × 4.5 =) 135 (litres)
(4.5 ÷ 0.2 =) 22.5 (seconds per gallon)
(0.2 ÷ 4.5 =) 0.044… (gallons per second)
(30 ÷ 0.2 =) 150
(0.2 × 60 = ) 12 (litres per minute)
(30 × 4.5 ÷ 60 =) 2.25
((30 ÷ 0.2) ÷ 60 =) 2.5
((4.5 ÷ 0.2) ÷ 60 =) 0.375 (minutes per gallon)
FT from an incorrect division or multiplication for further appropriate product or division correctly evaluated